I think to get around the kind of issue you describe I'll need to not have too much involvement between characters in any one character's playthrough, which I think may not be how you were envisioning your version of this kind of scenario in your game . My characters will be operating in the same timeline, but with their own missions and paths that are not necessarily intertwined in each level. Eg when playing A, you won't often be directly involved with B and C in the same level at all. A is flying to some position to recover Blue Widget while B would be staying behind to defend their main ship. Because each character as I envision it now has their own "job" (eg A is a Scout, B is a Defender/Fighter), they will have different kinds of missions and objectives that are designed for their role and while they'll be going through the same journey from Day 1 to Day X, they will (mostly) be doing so in different locations, scenarios, and kinds of objectives.
Fair enough
Keeping character-level interaction low certainly simplifies things. But in that case what will be the story that is told from different perspectives?
- Backstory - just reveal different pieces of full puzzle in different paths. IMHO backstories are overused - but they may also be very addictive if you have/are a good writer.
- No story at all - only general references to previous missions. Links between playthroughs are implemented simply via game mechanics.
The second variant is more interesting for me (although you can probably mix tory and game mechanics too).
For example it can be used to make quite logical level/difficulty system. At first playthrough you are completely free to choose pacing, mission order and so on. On second you are constrained by previous one. On third you are constrained by both previous one etc.